1. GRAVITY

2. EARTH’S GRAVITY FIELD ELLIPSOID 983 Gals 978 Gals 1 Gal = 1 cm/sec²
North-South change
~1 mGals/km
~1.5 mGals/mile
~1 Gals/m
~.3 Gals/ft

3. MEASURING GRAVITY ABSOLUTE VS RELATIVE
FG-5
A-10
Absolute
Pendulum
Weight Drop
Rise and Fall
Weight Drop

4. Relative GRAVIMETERS Stable Astatic Worden La Coste Romberg
Scintrex Auto Grav
Worden Gravity Meter

5. La Coste & Romberg
Zero length spring
T proportional L

8. Planning a Survey GRAVITY FIELD METHODS
Previous data – quality and quantity – target vs station density vs dollar$.
Instrumentation and field procedures
Acquiring permits, field preparations, low profile
Locations
Base ties, reocccupations, calibration, drift tares and tides
Special considerations in microgal surveys
Typical field procedures
Pitfalls and disasters (ignoring the above)

9. COMPUTING OBSERVED GRAVITY (MEASURED)
CORRECT METER READINGS FOR TIDES.
Earth Tides.
Caused by pull of sun and moon
Maximum change ~360Gals/6 hours = 1Gal/minute
Correction from recording gravimeter $, tidetables (obsolete), computer program
Computer Tide Corrections (Examples)

10. SAGE 2004 TIDE CORRECTIONS
NOTE: MAXIMUM
AMPLITUDE OF
~320GALS

11. SAGE 2013 TIDE CORRECTION

12. SAGE 2016 TIDE CORRECTION

13. COMPUTING OBSERVED GRAVITY TIDE AND DRIFT CORRECTIONS
CAUSED BY LONG TERM RELAXATION
ASSUMED TO BE SMOOTH, SLOW AND LINEAR
ESTIMATE BY REOCCUPATION OF BASE
CHECK FOR QUALITY CONTROL ON REOCC.

14. COMPUTING OBSERVED GRAVITY
OBSG = (SCMR – BCMR)GRCAL + ABGV
Where:
OBSG = Observed gravity
SCMR = Station corrected* meter reading
BCMR = Base corrected* meter reading
*Corrected for Drift and Tides
ABGV = Absolute base gravity value
GRCAL= Gravimeter calibration

15. GRAVITY REDUCTION (MODEL)
ELLIPSOID
TOPO SURFACE
GEOID
GEOID – Theoretical sea level surface.
ELLIPSOID – Mathematical model of the earth
(from satellites)
SPHEROID – Clark spheroid ~ 1866
(from land surveys)
GEOID
HEIGHT
EARTH’S
SURFACE
GEOID
ELLIPSOID

16. THEORETICAL GRAVITY (MODEL)
Geodetic Reference System (GRS) formulae refer to theoretical estimates of the Earth’s shape.
From these GRS formulae we obtain International Gravity Formulae (IGF)
Several different formulae have been adopted over the years
1930 – First internationally accepted IGF (Geoid based)
THEOG30 = ( sin²θ sin² 2θ)
1967 – Correction for Potsdam (Geoid based)
THEOG67 = ( sin²θ sin4θ)
1984 – Based on GRS 1980 – World Geodetic System (WGS84)
THEOG84 = ( sin²θ)
( sin²θ)
Requires correction for atmosphere (ATMCR).
ATMCR = 0.87e-0.116h (SL =0.87, 5 km =0.47, 10 km = 0.23 mGals)

17. GRAVITY ANOMALIES = MEASURED-MODEL
Free Air Anomaly (FAAyy)
FAAyy = OBSG-THEOGyy+FACu x SELEVu
FACu = Free air correction in feet or meters
SELEVu = Station elevation in feet or meters
FACf = ( sinθ² SELEVf) = ~ SELEVf
FACm = ( sinθ² SELEVm)
SELEVf = Station elevation in feet
SELEVm = Station elevation in meters
Simple Bouguer Anomaly (SBAyy)
SBAyy = FAAyy-BSCu
BSCu = Bouguer Slab Correction in feet or meters
BSCf = (2π6.6720.3048/1000.0)SELEVf = SELEVf
BSCm = (2π6.672/1000.0)SELEVm = SELEVm
Note (FACu - BSCu) ≈ 0.06 mGals/ft ≈ 0.20 mGals/meter
Complete Bouguer Anomaly (CBAyy)
CBAyy = SBAyy + TC
TC = Terrain Correction (usually calculated in two parts)

20. COMPLETE BOUGUER ANOMALIES OF THE UNITED STATES

21. ISOSTATIC ANOMALIES (PRATT – AIRY)
c=density of crust
w=density of sea water
s=density of substratum
h=density of crust –mountains
o=density of crust-oceans
r=density of crust-ridge

22. 100% COMPENSATION

23. 75% COMPENSATION

24. 0% COMPENSATION

25. REGIONAL- RESIDUAL GRAVITY ANOMALIES
DEFINITION:
RESIDUAL = COMPLETE BOUGUER-REGIONAL
REGIONAL ANOMALY IS DETERMINE BY SCALE OF THE TARGET. (NON UNIQUE)
SEPARATION METHODS:
LINEAR SEPARATION (PROFILE METHOD 1D)
MAP SEPARATION (2D)
LEAST SQUARES FIT OF GRAVITY ANOMALIES

26. LINEAR SEPARATION

27. COMPLETE BOUGUER ANOMALY REGIONAL ANOMALY
MAP SEPARATION
COMPLETE BOUGUER ANOMALY REGIONAL ANOMALY
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28. RESIDUAL BOUGUER ANOMALY5

29. LEAST SQUARES FIT OF STATION GRAVITY
PROBLEM: PRODUCE A REGULAR GRID OF GRAVITY VALUES FROM A RANDOMNLY DISTRIBUTED DATA SET.

30. LEAST SQUARES FIT OF STATION GRAVITY
General quadric function of form:
F(x,y) = Ax² +By² +Cxy +Dx + Ey +F
Weighting function of form:
W = ((R-di)/di)n

31. DOMAIN RADIUS (R) + + + + + + + + + + + + + + + + + + + + + + + + R di

32. REGIONAL - RESIDUAL Mean Value Theorem Use LSF Grid
Select a Separation Width
Similar to Griffin Method (use circle)
Rapid Calculations
Produce Suite of Regional/ Residual Maps